On exponential modified gravity

TL;DR

This paper explores a modified gravity model with an exponential function of Ricci scalar, analyzing its stability, cosmological solutions, and local tests, and finds constraints on parameters ensuring consistency with observations.

Contribution

The paper introduces and analyzes a novel exponential form of $F(R)$ gravity, deriving stability conditions, scalar field potentials, and cosmological solutions, with bounds from local tests.

Findings

Parameter $eta$ constrained to $eta imes 10^{-6}$ cm$^2$ from local tests.

De Sitter space is unstable, zero curvature solutions are stable.

Model passes matter stability test.

Abstract

A modified theory of gravity with the function $F(R) = R\exp(\alpha R)$ instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and analyzed. The action of the model is converted into Einstein$-$Hilbert action at small value of the parameter $\alpha$. From local tests we obtain a bound on the parameter $\alpha\leq 10^{-6}$ cm$^2$. The Jordan and Einstein frames are investigated and the potential of the scalar field in Einstein's frame is found. The mass of a scalar degree of freedom as a function of curvature is obtained. The static solutions of the model are found corresponding to the Schwarzschild$-$de Sitter space. We show that the de Sitter space is unstable but a solution with zero curvature is stable. The cosmological parameters of the model are calculated. It was demonstrated that the model passes the matter stability test.